On a Generalized Briot-Bouquet type Differential Subordination

2021/01/02 by S. Sivaprasad Kumar, Kumar, S. Sivaprasad, Priyanka Goel +1
Mathematics · Physics and Astronomy · #Analytic and geometric function theory #Nonlinear Waves and Solitons #math.CV

paper · pdf · doi:10.48550/arxiv.2101.00353

arxiv created 2022/03/11 · arxiv updated 2022/03/14

Abstract

We introduce and study the following special type of differential subordination implication: p(z)Q(z)+(zp'(z))/(βp(z)+α)\prec h(z) ⇒ p(z)\prec h(z), which generalizes the Briot-Bouquet differential subordination, where Q(z) is analytic and 0≠β,α∈ℂ. Further, some special cases of our result are also discussed. Finally, analogues of open door lemma and integral existence theorem with applications to univalent functions are obtained.

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